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Question
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Determine the speed at which the kinetic energy of an electron is equal to three times its rest energy.
Answer : 0.97c
From special thoery of relativity
E = K.E+mc2
K.E =3mc2
mc2 = 2m c2+mc2 =3 mc2
=4
= 1/[1-(v2/c2)]1/2
42 = 1/[1-(v2/c2)]
1-(v2/c2) =1/16
(v2/c2) = 1-1/16 =15/16
v/c = 0.9682458
v =0.97 c(2dp)